Merge algorithm: Difference between revisions

Revision as of 08:28, 11 March 2019

Revision as of 14:08, 4 May 2019

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merge(A[r+1...j], B[s...ℓ], C[t+1...q])

The algorithm operates by splitting either {{mvar|A}} or {{mvar|B}}, whichever is larger, into (nearly) equal halves. It then splits the other array into a part thatwith isvalues smaller than the midpoint of the first, and a part that iswith larger or equal values. (The [[binary search]] subroutine returns the index in {{mvar|B}} where {{math|''A''[''r'']}} would be, if it were in {{mvar|B}}; that this always a number between {{mvar|k}} and {{mvar|ℓ}}.) Finally, each pair of halves is merged [[Divide and conquer algorithm|recursively]], and since the recursive calls are independent of each other, they can be done in parallel. Hybrid approach, where serial algorithm is used for recursion base case has been shown to perform well in practice <ref name="vjd">{{cite| author=Victor J. Duvanenko| title=Parallel Merge| journal=Dr. Dobb's Journal| date=2011| url=http://www.drdobbs.com/parallel/parallel-merge/229204454}}</ref>

The [[Analysis of parallel algorithms#Overview|work]] performed by the algorithm for two arrays holding a total of {{mvar|n}} elements, i.e., the running time of a serial version of it, is {{math|''O''(''n'')}}. This is optimal since {{mvar|n}} elements need to be copied into {{mvar|C}}. Its critical path length, however, is {{math|Θ(log² ''n'')}}, meaning that it takes that much time on an ideal machine with an unbounded number of processors.{{r|clrs}}{{rp|801–802}}